US7295954B2  Expert knowledge methods and systems for data analysis  Google Patents
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Abstract
Description
This application claims priority from U.S. Provisional Patent Application No. 60/414,021 filed on Sep. 26, 2002, and entitled “Method for Quantifying Uniformity Patterns and Including Expert Knowledge for Tool Development and Control,” which is incorporated herein by reference in its entirety.
1. Field of the Invention
The present invention relates generally to methods for analyzing the performance of wafer process operations run on wafer processing equipment, and more particularly, to methods for identifying variables that cause outofstatisticalcontrol signals and techniques for incorporating expert knowledge to ascertain the significance of such signals.
2. Description of the Related Art
In an attempt to quantify and study the effects of process conditions during wafer processing, process engineers are tasked with running numerous process runs, each with particularly set variables, and then comprehensively studying results. The set variables, as is well known, are many. For instance, variables can include chamber pressure, chamber temperature, the delivered power to one or both electrodes, electrostatic chuck clamping voltage, types of gases and flow rates, etc. In practice, therefore, data for such variables is measured and recorded as wafers are put through process runs. Databases are created to organize the data for such variables. In the analysis of such data, specific attention is paid to ascertain whether the behavior of particular variables is within an acceptable range.
Multivariate statistical process control tools are available for the monitoring of deviations between historical process runs and new process runs. These tools can statistically define normal operating behavior in a process based on historical data. Statistical projectionbased techniques, such as principal component analysis (PCA), are used to produce outofstatisticalcontrol signals when a variable is identified as deviating out of the bounds of normal operating behavior.
As multivariate statistical process control tools accommodate analysis across a large number of variables the resulting models are very sensitive, too sensitive with respect to some variables.
Another challenge associated with using these techniques is to determine if an out of bounds signal is considered meaningful based on expert knowledge. Some variables or ranges of variable values are more critical than others. For example, once a wafer is clamped into position the clamp voltage could vary, yet still not be considered a fault, or error in the system. Generally, faults are generated when a value for a variable changes so much that it falls outofstatistical control. So, if a value for clamp voltage is recorded as being out of an acceptable statistical bounds relative to other variables in the system, it may be flagged as a problem and an automatic fault code would be sent out halting the wafer processing.
However an expert observing the same value for clamp voltage might not be concerned with the variable deviation. For example, though the value for clamp voltage is out of the acceptable statistical bounds it could still fall in an operating range where the clamp properly holds the wafer. Unfortunately, a fault would still be registered, even though expert knowledge would deem the out of bounds signal as not warranting a fault. The end result is that reliance on pure mathematical statistical analysis will lead to false fault alarms. Nevertheless, during processing, every fault will generally lead to stoppage of wafer processing operations, thus resulting in wasted time and money.
The models generated in statistical projectionbased techniques can be made more robust by incorporating large amounts of data for a particular process and by incorporating detailed information for each variable being recorded. The limitation with this approach is that during the phase when models are being built large amounts of data are not always available for the variables and the cost of experimental operation can be very impractical.
In view of the foregoing, what is needed is a method and system for incorporating expert knowledge in the identification and reduction of false fault alarms in wafer processing systems.
Broadly speaking, the present invention fills this need by providing a method and system for incorporating expert knowledge for the identification of unimportant outofstatisticalcontrol signals in wafer processing systems. Several embodiments of the invention are described below.
In one embodiment, a method for adjusting a data set defining a set of process runs, each process run having a set of data corresponding to a set of variables for a wafer processing operation is provided. A model derived from a data set is received. A new data set corresponding to one process run is received. The new data set is projected to the model. An outlier data point produced as a result of the projecting is identified. A variable corresponding to the one outlier data point is identified, the identified variable exhibiting a high contribution. A value for the variable from the new data set is identified. Whether the value for the variable is unimportant is determined. A normalized matrix of data is created, using random data and the variable that was determined to be unimportant from each of the new data set and the data set. The data set is updated with the normalized matrix of data.
In another embodiment, a method for adjusting a data set defining a set of process runs, each process run having a set of data corresponding to a set of variables for a wafer processing operation is provided. A model derived from a data set is received. A new data set is received. The new data set is projected to the model. Outlier data points produced as a result of the projecting are identified. One of the outlier data points from the outlier data points is identified. A variable corresponding to the one outlier data point is identified, the identified variable exhibiting a high contribution. Whether the variable is unimportant is determined. A normalized matrix of data is created, using data from the new data and from the data set, the normalized matrix of data created using the variable that was determined to be unimportant from each of the new data and the data set. The data set is updated with the normalized matrix of data.
In accordance with another aspect of the present invention, a method for updating a data set defining a set of process runs, each process run having a set of data corresponding to a set of variables for a wafer processing operation is provided. A data set is received. Scaling to the data set is performed. Principal component analysis is performed to the scaled data set to generate a model. New data is received. The new data is projected to the model. Outlier data points based on the projecting are identified. A contribution plot corresponding to one of the outlier data points is examined. A variable that corresponds to the one outlier data point which provides a high contribution in the contribution plot is identified. That the variable is unimportant is determined. A desensitizing set of data for the variable is created based on a standard deviation of the data set and a randomization of the new data. The data set is augmented with the desensitizing set of data.
In one embodiment, a method for adjusting a data matrix defining a set of process runs each process run having a set of data corresponding to a set of variables for a wafer processing operation is provided. A data matrix of N rows and M columns where N equals a number of process runs and M equals a number of variables in the data matrix is received. A new set of data with M variables wherein at least one variable corresponds to an outlier and is unimportant based on expert input is received. A normally distributed random vector containing N−1 rows is generated. A one vector containing N−1 rows of ones is generated. A standard deviation of data corresponding to the variable in the data matrix is determined. The standard deviation is multiplied by the normally distributed random vector producing a first vector. The data corresponding to the variable from the new data is multiplied by the one vector producing a second vector. The first vector is added to the second vector producing a third vector. An expert desensitizing matrix is created where the Mth column contains the third vector and the remaining columns are made up of data corresponding to the remaining variables. A new data matrix is created where the data matrix is augmented by the expert desensitizing matrix.
The advantages of the present invention are numerous. One notable benefit and advantage of the invention is that data sets of process runs in wafer process systems can be desensitized incorporating expert knowledge to unimportant variable data by incorporating smaller amounts of data.
Other advantages of the invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the invention.
It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not restrictive of the invention, as claimed.
The accompanying drawings, which are incorporated in and constitute part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the principles of the invention.
Several exemplary embodiments of the invention will now be described in detail with reference to the accompanying drawings.
Once the data set is received, the method advances to operation 112 in which scaling is performed on the data set. In one embodiment, the data set can be autoscaled such that each variable is in standard units (i.e., has a zero mean and a unit standard deviation) to ensure that the data can be compared across variables with different units. Assuming the data set has been scaled, the method advances to operation 114.
In operation 114 principal component analysis (PCA) is performed on the scaled data set to produce a PCA model and multivariate statistical numbers (such as, for example, Qresidual, T^{2 }residual) of the data set. Multivariate statistical process control is used to define normal operating behavior in a process by statistically analyzing the data from the process. Principal component analysis (PCA) is a statistical projectionbased technique, which enables the detection of outofstatisticalcontrol signals in a process. PCA provides a statistical evaluation of the data set. Modeling methods used for multivariate statistical process control, other than PCA, could be used in this step as well. The PCA performed on the scaled data set will provide a statistical evaluation of the data set that includes a PCA model.
After the principal component analysis has been performed on the scaled data set, the method advances to operation 116. In operation 116 a model is received. The model received is the PCA model which is a result of the PCA operation performed on the data set in operation block 114. Once the model is received, the method advances to operation 118.
In operation 118, a new data set is received. The new data set received in operation 118 is new data corresponding to one process run in a wafer processing system having the same set of variables as the original data set received in operation 110. This method could also be used for a new data set composed of more than one process run. Once the new data set is received, the method advances to operation 120.
In operation 120, the new data set is scaled and projected to the model. In the embodiment shown in
The projection of the new data set to the model will provide a residual plot with corresponding variable contribution plots. These plots will provide statistical information regarding the relationship between the new data set from operation 118 and the data set from operation 110. The residual plot will show if the new data set for the new process run from operation block 118 corresponds to a statistical outlier relative to the multivariate mean, multivariate variation, and a chosen confidence bounds for the data set from operation 110. In this embodiment, the residual plot used is the Qresidual plot. In another embodiment, the residual plot used is the T^{2 }residual plot.
Assuming the new data set has been projected to the model, the method advances to operation 122. In operation 122, the residual plot produced when the new data set was projected to the model is examined to determine if an outlier data point or points exist. For a new data set containing more than one process run, each process run will correspond to a single data point on the residual plot. If the new data set point falls out of an acceptable range of the Qresidual of the data set from operation 110 (i.e., is out of bounds with respect to the model confidence limit), then an outlier exists. Once the determination whether an outlier exists has been made, the operation will proceed to either operation block 124 if an outlier does not exist or to operation block 126 if an outlier does exist.
If an outlier does not exist in the residual plot examined in operation block 122, the method advances to operation 124. In operation 124, the new data set is incorporated with the data set received in operation 110 to create an expanded data set. This expanded data set is then sent to operation block 110 and the method begins again from operation block 110.
If an outlier does exist in the residual plot examined in operation block 122, the method advances to operation block 126. In operation 126, the contribution plot that corresponds to the outlier data point identified in operation 122 is examined for a variable contributor with a high contribution. The residual plot produced after the new data set is projected onto the model in operation 120 will contain one data point for each process run of the new data set. Each data point on the residual plot will then in turn have an associated contribution plot. Each contribution plot will show the relative contribution for each variable's contribution to the QResidual. If a variable has a high relative contribution then it is identified as a variable contributor with a high contribution. Whether a contribution is high is a subjective determination. For this example we will assume that there is only one variable contributor with a high contribution. However the contribution plot can have more than one variable contributor and can be accommodated by the method as will be discussed below. Once the contribution plot is examined and a variable is identified as providing a high contribution the method advances to operation block 128.
In operation 128, expert knowledge is used to determine if the variable or the value of the variable identified as providing a high contribution is considered unimportant. Here expert knowledge is information regarding the variables or the value of the variables. An expert is, in this example, an engineer that has extensive knowledge and experience regarding the significance of each variable. Thus, if the variable contributor is determined to be, for example, the wafer clamp voltage variable, the expert might consider this variable to be an unimportant variable.
Furthermore, the expert knowledge might deem a certain range of values for wafer clamp voltage to be acceptable, even if the value is out of acceptable statistical bounds. For example, the wafer clamp voltage could be within engineering specifications. Therefore a fault should not be called in the system based on the given value for the wafer clamp voltage. In this case, the expert knowledge would label a particular range of values for the variable as unimportant. If the value of the variable is considered by the expert knowledge to actually necessitate causing a fault, then after operation block 128 the method will advance to operation block 130. In operation block 130, the detected out of statistical bounds variable will trigger a fault. Alternatively, if the expert knowledge labels the variable or the value of the variable as unimportant, then the method will proceed to operation block 132.
In operation 132, an expert randomizer (ER) will be implemented to create a desensitizing matrix, and then the desensitizing matrix will be augmented to the data set originally received in operation block 110. The expert randomizer implements a method that normalizes the new data corresponding to the variable by using normally distributed random data and the variable data from the data set along with the variable data from the new data. In the embodiment shown in
The desensitizing matrix will desensitize the data set with respect to the value of the variable in the new data, such that if the same variable data is seen in a subsequent set of new data the same variable data will not cause an outlier in a residual plot when the new data is projected onto the PCA model. Utilizing the teachings of this invention is significantly improved over prior art embodiments that perform trivial desensitization by removing a variable or variables that cause the data to be an outlier from the analysis entirely. This is an important distinction, as the removal of variables eliminates the ability to continue detecting outliers based on those particular variables. According to the teachings of this invention, such outliers can still be detected at levels of deviation above the desensitization level, which is still very valuable.
One of the strengths of multivariate statistical models for fault detection is the quantification of fault behaviors involving correlated changes amongst the variables. These correlations and their relative sensitivities to variable deviations are referred to as the “structure” of the model which can be visually assessed by comparing the loads of the variables in the model. Another advantage inherent in the methods of this invention is that the model is desensitized to deviations in a variable or variables without destroying the structure of the model, which can be seen in
After the data set originally received in operation block 110 is augmented by the desensitizing matrix, the resulting matrix of data will be sent to operation block 110 to begin the method again if necessary.
An example illustrating the methodology described above as applied to a new data set having more than one process run will be discussed next, with reference to
As shown in
The variable contribution of the exemplary 44^{th }process run is shown in variable contribution plot 170. The relative contribution of variable four (4) 175 is high. For this example there is only one variable with a high contribution, but in other embodiments there could be more than one variable being a high contributor. After variable four has been identified in contribution plot 170 as having a high contribution, expert input will be sought to determine if variable four is unimportant (i.e., if the value for variable four, though causing an outlier, is still acceptable and should not be labeled as a fault). Assuming that variable four is deemed as unimportant based on expert knowledge, the new data set will be normalized. Here, an expert randomizer is used to adjust the new data set. One embodiment of an expert randomizer will be provided in more detail below.
Once the expert randomizer has been applied to create a desensitizing matrix and the data set is augmented with this desensitizing matrix the method can be run again with the augmented data set. If the method is run again with a new data set having the same values as the first new data discussed above, the variable four data will not cause an outlier. The outlier behavior of the variable four data will be desensitized out of the data set. The result of running the method again using the data set augmented with the desensitizing matrix, and introducing a new data set identical to the 44 process run data set used above, will be shown in a sidebyside residual plot.
The embodiment of the invention works more efficiently if the variable at issue, such as variable four above, does not have a strong correlation with the other variables in the process run. The correlation across the variables can be checked with the use of a correlation coefficient chart. A correlation coefficient chart is provided for the example discussed in
Exemplary code for an expert randomizer is provided in the following tables. In Table 1 below, the code provides for the case when the new data set is composed of one sample, i.e., one process run. Table 2 below provides for the case when the new data set is composed of multiple samples, i.e., more than one process run. Both Table 1 and Table 2 provide for the case when one or more variables is identified to be desensitized within a single process run of new data. The MATLAB® variable definitions are provided in the Notations section. Note that although MATLAB® is used, any appropriate software language to carry out the functionality could be used to create an expert randomizer.
TABLE 1  
EXPERT RANDOMIZER MATLAB ROUTINE  
Case1: Exemplary code for one sample of new data  
ED=zeros(m,n); % assigning/initializing ED to be a matrix of zeros  
of size mbyn  
ED(1,:)=x; % assigning 1^{st }row of ED as the new sample  
for j=1:kn % starts the loop for generating an expert data matrix  
for each variable to be  
desensitized  
NDR=randn(m1,1); % generating a normally distributed  
random columnvector  
O=ones(m1,1); % generating a columnvector of ones  
for computation  
r(:,j)=s(1,p(j))*NDR + x(mm,p(j))*O; % calculating the  
new value of the variable to  
be desensitized based on expert knowledge  
if p(km,j)>1 % checking if the variable to be discarded  
is not the first variable in the  
matrix  
for i=2:m % loop for replicating the samples  
ED(i,1:p(j)−1)=x(mm,1:p(j)−1);  
ED(i,p(j)+1:end)=x(mm,p(j)+1 :end);  
end  
elseif p(km,j)==1 % checking if the variable to be discarded  
is the first variable in  
the matrix  
for i=2:m  
ED(i,p(j)+1:end)=x(mm,p(j)+1:end); % assigning  
the values of variables not  
being desensitized  
end  
end  
end  
for pp=1:kn  
ED(2:m,p(pp))=r(:,pp); % assigning the values of  
variables being desensitized  
end  
Data=[Data;ED]; % augmenting the original data matrix  
to include the new matrix  
Notations:  
Data: matrix containing original data which is imported  
m: number of samples in the original data  
n: number of variables in the original data  
x: matrix containing new data, which is imported  
mm: number of samples in the new data having same number of variables (n)  
p: index of variables that are determined as unimportant and have high contributions  
kn: number of variables to discard that are not correlated strongly to other variables  
km=1, number of rows for discarded vector  
s: standard deviation of the variables in the original data, which is imported  
NDR: normally distributed random vector of size mby1  
O: vector of ones of size mby1  
r: column vector that is being calculated based on expert knowledge  
ED: Expert Data matrix 
TABLE 2  
EXPERT RANDOMIZER MATLAB ROUTINE  
Case2: Exemplary code for any number of samples of new data.  
ED=zeros(2*mm,nn); % assigning/initializing ED to be a  
matrix of zeros of size mbyn  
ED(1:mm,1:nn)=x; % assigning first row of ED  
as the new sample  
for j=1:kn % starts the loop for generating an expert data  
matrix for each variable to be  
desensitized  
NDR=randn(mm,1); % generating a normally distributed  
random columnvector  
O=ones(mm,1); % generating a columnvector of ones  
for computation  
r(:,j)=s(1,p(j))*NDR + x(mm,p(j))*O; % calculating the  
new value of the variable to  
be desensitized based on expert knowledge  
if p(km,j>1 % checking if the variable to be discarded is not  
the first variable in the  
matrix  
for i=mm+1:2*mm % loop for replicating the samples  
ED(i,1:p(j)−1)=x(i−mm,1:p(j)−1);  
ED(i,p(j)+1:end)=x(i−mm,p(j)+1:end);  
end  
elseif p(km,j)==1% checking if the variable to be discarded  
is the first variable in the  
matrix  
for i=mm+1:2*mm  
ED(i,p(j)+1:end)=x(i−mm,p(j)+1:end); %  
assigning the values of variables not  
being desensitized  
end  
end  
end  
for pp=1:kn  
ED(mm+1:2*mm,p(pp))r(:,pp); % assigning the values of  
variables being  
desensitized  
end  
Data=[Data;ED]; % augmenting the original data  
matrix to include the new matrix  
Notations:  
Data: matrix containing original data, which is imported  
m: number of samples in the original data  
n: number of variables in the original data  
x: matrix containing new data  
mm: number of samples in the new data having same number of variables (n)  
p: index of variables that are determined as unimportant and have high contributions  
kn: number of variables to discard that are not correlated strongly to other variables  
km=1, number of rows for discarded vector  
s: standard deviation of the variables in the original data, which is imported  
NDR: normally distributed random vector of size mby1  
O: vector of ones of size mby1  
r: column vector that is being calculated based on expert engineer knowledge  
ED: Expert Data matrix 
Provided below is an example describing the execution of the Expert Randomizer MATLAB Routine provided in Table 1. In this example the new data set includes one sample (i.e., process run). Only one variable will be desensitized in this example. The example is generalized to provide and overall understanding of operation steps performed in the Expert Randoinizer MATLAB Routine provided in Table 1. The example may not include a description of every operation of the code.
Step 1
Certain MATLAB® variables are assigned values by importing data. (initializations not all shown in code). Data is the MATLAB® variable containing the original data for the wafer process system. The values of the original data are already known based on previous runs for the same process on the same equipment. The original data is imported into MATLAB® for use in the calculations. In this example the value for Data follows:
Data is represented by a matrix of m (=4) rows and n (=3) columns. Each column represents a variable in the wafer processing system (i.e., there are 3 variables in this example). Each row represents a sample (i.e., process run).
Step 2
The new data is represented by the MATLAB® variable x. The new data must contain the same number of variables (n=3) as the original data. The new data is imported into MATLAB® and initialized. For this example the value for each variable/column for the new data is:
x=10 200 3
Before the Expert Randomizer is initiated it is assumed that x has been determined to be an outlier (when compared to the original data, ‘Data’). Also, for this example the third variable has been assumed to be a high contributor and has been labeled as unimportant based on engineering knowledge.
Step 3
ED is initialized having the same size as the Data matrix (step 1), where each element is assigned a value of 0.
ED=zeros(m,n)
For this step the value for ED is:
Step 4
The first row of ED is assigned the values from the new sample, x
For this step the value for ED is:
Step 5
The standard deviation for Data is calculated. This standard deviation will be used to generate the expert randomizer.
s=std(Data)
std is a MATLAB® command that calculates the standard deviation of a matrix.
So, the value for s is shown below:
s=0.13 0.17 0.06
Each number in the s vector denotes the standard deviation for a variable in the Data matrix.
Step 6
Next, a normally distributed random vector with 3 rows is generated.
NDR=randn(3,1), where randn is a standard MATLAB® command that generates random data.
The value for NDR is shown below:
Step 7
A vector labeled O is generated. The O vector contains ones and has the same number of rows as NDR. This vector is used to facilitate with the matrix computations.
O=ones(3,1), where ‘ones’ is a standard MATLAB® command
The value for O is shown below:
Step 8
In this step the standard deviation of the third variable from Data (i.e., s(1,3)) is multiplied by NDR. The resulting value is added to the value for the third variable from the new data (x(1,3)).
r=s(1,3)*NDR+x(1,3)*O
This provides:
Step 9
Multiple copies of the new data, which is not being desensitized, are made and assigned to the second, third and fourth rows of the ED matrix
Step 10
The value for r is assigned to rows 2 through 4 of the third column of the ED matrix.
ED (2:4,3)=r
Therefore,
Step 11
Finally, ED is augmented to the Data matrix. This new matrix replaces Data.
 Data=[Data;ED]
Therefore,
As described, the Expert Randomizer provides a method for adjusting a new data set, which has met the outlier, high contribution, and expert knowledge criteria discussed above to then normalize the new data with respect to the original data set. The normalized data is then augmented to the original data set. So, the augmented data will have been desensitized to the variable data which initially caused an outlier.
Any of the operations described herein that form part of the invention are useful machine operations. The invention also relates to a device or an apparatus for performing these operations. The apparatus may be specially constructed for the required purposes, or it may be a generalpurpose computer selectively activated or configured by a computer program stored in the computer. In particular, various generalpurpose machines may be used with computer programs written in accordance with the teachings herein, or it may be more convenient to construct a more specialized apparatus to perform the required operations.
The invention can also be embodied as computer readable code on a computer, readable medium. The computer readable medium is any data storage device that can store data which can thereafter be read by a computer system. Examples of the computer readable medium include hard drives, network attached storage (NAS), readonly memory, randomaccess memory, CDROMs, CDRs, CDRWs, magnetic tapes, and other optical and nonoptical data storage devices. The computer readable medium can also be distributed over a network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion.
It will be further appreciated that the instructions represented by the operations in
In summary, the embodiments of the present invention provide a method for incorporating expert knowledge for the identification of unimportant outofstatisticalcontrol signals in wafer processing systems. The invention has been described herein in terms of several exemplary embodiments. Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention. The embodiments and preferred features described above should be considered exemplary, with the invention being defined by the appended claims and equivalents thereof.
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 20030926 AU AU2003299054A patent/AU2003299054A1/en not_active Abandoned
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Also Published As
Publication number  Publication date 

TWI235311B (en)  20050701 
TW200413951A (en)  20040801 
WO2004030082A1 (en)  20040408 
US20040064465A1 (en)  20040401 
EP1550155A1 (en)  20050706 
AU2003299054A1 (en)  20040419 
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